NISTIR 5880
Mathematical Analysis of Practices to Control Moisture in the Roof
Cavities of Manufactured Houses
D. M. Burch
Building and Fire Research Laboratory
Gaithersburg, Maryland 20899-0001
G. A. Tsongas
Mechanical Engineering Department
Portland State University
Portland, Oregon 97207
G. N. Walton
Building and Fire Research Laboratory
Gaithersburg, Maryland 20899-0001
United States Department of Commerce
Technology Administration
National Institute of Standards and Technology
NISTIR 5880
Mathematical Analysis of Practices to Control Moisture in the Roof
Cavities of Manufactured Houses
D. M. Burch, G.A. Tsongas, and G.N. Walton
September 1996
Building and Fire Research Laboratory
National Institute of Standards and Technology
Gaithersburg, Maryland 20899
U.S. Department of Commerce
Michael Kantor, Secretary
Technology Administration
Mary L. Good, Under Secretary for Technology
National Institute of Standards and Technology
Arati Prabhakar, Director
Prepared for:
U.S. Department of Housing
And Urban Development
Washington, D.C. 20410
TABLE OF CONTENTS
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
KEYWORDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Basic Transport Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Ventilated Cavity Moisture and Heat Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Airflow from House into Attic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Roof Cavity Ventilation Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Indoor Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Outdoor Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Indoor Temperature and Humidity Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Solution Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
DESCRIPTION OF CURRENT PRACTICE HOUSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
PARAMETERS USED IN ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Water Vapor Diffusion Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Liquid Diffusivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Airflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Other Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Indoor and Outdoor Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
COLD CLIMATE RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Performance of Current-Practice House in Madison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Effect of Roof Cavity Ventilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Effect of a Ceiling Vapor Retarder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Effect of Airflow from House into Roof Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Effect of Indoor Relative Humidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Effect of Outdoor Climate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Other Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Summary of Effect of Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
PROVIDING WHOLE HOUSE VENTILATION WITH CEILING VENTS . . . . . . . . . . . . . . . 36
i
EFFECTIVENESS OF MOISTURE CONTROL PRACTICES IN COLD CLIMATES . . . . . 40
Tight House with High Moisture Generation Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Humidified House . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
AN ALTERNATIVE ATTIC MOISTURE CONTROL PRACTICE IN COLD CLIMATES . . 42
EFFECTIVENESS OF CURRENT MOISTURE CONTROL PRACTICES IN HOT AND
HUMID CLIMATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
RECOMMENDATIONS FOR FURTHER STUDY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Model Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Roof Moisture Performance in Different U.S. Climates . . . . . . . . . . . . . . . . . . . . . . . . . 47
Uncertainties Regarding Attic Ventilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Shingle Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
SUMMARY AND CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
LIST OF TABLES
Table 1. Number of Finite-Difference Nodes in Roof Construction . . . . . . . . . . . . . . . . . . . . . 12
Table 2. Sorption Isotherm Regression Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Table 3. Permeability Regression Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Table 4. Effect of Parameters on Roof Sheathing Moisture Content . . . . . . . . . . . . . . . . . . . . . 38
LIST OF FIGURES
Figure 1
Flow chart of thermal solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Figure 2
Flow chart of moisture solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Figure 3
Half cross-section of roof cavity of double-wide manufactured house . . . . . . . . . . . 13
ii
Figure 4
Sorption isotherms of the materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Figure 5
Water vapor permeances of materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Figure 6
Volumetric attic ventilation rate per unit roof effective leakage area plotted as a
function of wind speed [measurements taken from Buchan, Lawton, Parent Ltd.
(1991)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Figure 7
Surface moisture content of roof cavity construction materials for the current practice
house . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Figure 8
Effect of passive roof cavity ventilation on the moisture content of north-sloping
plywood roof sheathing for current practice house . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Figure 9
Effect of mechanical roof cavity ventilation on the moisture content of north-sloping
plywood roof sheathing for current practice house . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Figure 10 Effect of an interior ceiling vapor retarder on the moisture content of north-sloping
plywood roof sheathing for current practice house . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Figure 11 Effect of airflow from house into roof cavity on the moisture content of north-sloping
plywood roof sheathing for current practice house . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Figure 12 Effect of indoor humidification on the moisture content of north-sloping plywood
roof sheathing and indoor relative humidity for current practice house
a. Surface moisture content
b. Indoor relative humidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Figure 13 Effect of moisture production rate on the moisture content of north-sloping plywood
roof sheathing and indoor relative humidity for current practice house
a. Surface moisture content
b. Indoor relative humidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Figure 14 Effect of house tightness on the moisture content of north-sloping plywood roof
sheathing for current practice house . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Figure 15 Effect of indoor mechanical ventilation on the moisture content of north-sloping
plywood roof sheathing and indoor relative humidity for current practice house
a. Surface moisture content
b. Indoor relative humidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
iii
Figure 16 Effect of outdoor climate on the surface moisture content of north-sloping plywood
roof sheathing and indoor relative humidity for current practice house
a. Surface moisture content
b. Indoor relative humidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Figure 17 Effect of other factors on the surface moisture content of north-sloping plywood roof
sheathing for current practice house
a. Indoor temperature
b. Sky radiation
c. Roof solar absorptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Figure 18 Effect of ceiling vents on the moisture content of north-sloping plywood roof
sheathing, airflow, and indoor relative humidity for current practice house
a. Surface moisture content
b. Airflow from house into roof cavity
c. Indoor relative humidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Figure 19 Effectiveness of roof cavity vents in tight house with high moisture production rate 41
Figure 20 Effectiveness of roof cavity vents in a humidified house . . . . . . . . . . . . . . . . . . . . . 43
Figure 21 Effectiveness of sealing air leakage paths in the ceiling construction of the tight house
with high moisture generation rate as alternative moisture control practice
a. Surface moisture content
b. Ceiling airflow rate
c. Indoor relative humidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Figure 22 Effectiveness of current HUD Standards moisture control practices in a hot and humid
climate
a. With a ceiling vapor retarder
b. Without a ceiling vapor retarder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
iv
ABSTRACT
A mathematical model is presented that predicts moisture and heat transfer in ventilated cavities such
as attics, roof cavities, and cathedral ceilings. The model performs a transient moisture and heat
balance as a function of time of year and includes the storage of moisture and heat at the construction
layers. The model includes both molecular diffusion and capillary transfer within the materials.
Radiation exchange among the ventilated cavity surfaces is predicted using a mean-radianttemperature-network model. Latent heat (i.e., the effect of water evaporating from one place and
condensing at another place) is distributed within the materials. Airflow from the house into the
ventilated cavity is predicted using a stack effect model with aggregated effective leakage areas. Air
exchange between the ventilated cavity and outdoor environment is predicted by a semi-empirical
model. The relative humidity in the house is permitted to vary during the winter and is calculated
from a moisture balance of the whole building.
This mathematical model was used to simulate the performance of a double-wide manufactured
house constructed in compliance with the latest HUD Standards. An interior vapor retarder was
installed in the ceiling construction and ventilation openings were installed in the roof cavity
consistent with the 1/300 rule given in the HUD Standards. The effect of passive and mechanical
ventilation, as well as a wide range of other factors on the roof sheathing moisture content was
investigated as a function of time. The weekly average moisture content of the lower surface of the
plywood sheathing was analyzed in several cold climates, while the relative humidity at the lower
surface of the ceiling insulation was analyzed in a hot and humid climate.
The analysis revealed the following: 1) airflow from the house into the roof cavity, as opposed to
water-vapor diffusion, was the dominant moisture transport mechanism into the roof cavity; 2) high
roof sheathing moisture content occurred in houses having high indoor relative humidity (i.e., high
moisture production rate, or tight construction, or both); 3) passive roof cavity vents consistent with
the 1/300 rule were found to maintain the roof sheathing moisture content in non-humidified houses
below fiber saturation during the winter; 4) the mechanical roof cavity ventilation rate specified in
the HUD Standards for removing moisture during the winter was found to be too small and thus
needs to be revised; 5) the presence of a ceiling vapor retarder was found to provide very small
reductions in roof sheathing moisture content; 6) when an interior vapor retarder was installed in the
ceiling construction of an air-conditioned house exposed to a hot and humid climate, the relative
humidity at its upper surface rose above 80%, thereby providing a conducive environment for mold
and mildew growth; and 7) the use of ceiling vents to provide additional whole house ventilation in
cold climates substantially increased the roof sheathing moisture content of a house with an
unventilated attic. Recommendations for further study are presented.
KEYWORDS
Airflow, Attic Ventilation, Attics, Building Technology, Ceiling Vents, Guidelines and Practices,
HUD Standards, Manufactured Housing, Mathematical Analysis, Moisture, Moisture Analysis,
Moisture Control, Moisture Modeling, Roof Cavities and Roof Ventilation.
1
INTRODUCTION
During the winter, moisture released by occupant activities causes the absolute humidity (or water
vapor pressure) inside a manufactured house to be higher than that of the outdoor air. This vapor
pressure potential causes water vapor to diffuse through the ceiling construction into the roof cavity.
In addition, a buoyant force (i.e., the stack effect) causes airflow from the house into the roof cavity1
through cracks and penetrations (e.g., ceiling light fixtures, plumbing and HVAC penetrations, and
cracks above interior partition walls). A portion of this moisture is removed by attic ventilation. The
remainder becomes absorbed or condenses onto the cold interior surfaces of the roof cavity (most
important of which is the plywood roof sheathing).
It is possible for the moisture content of the roof sheathing to rise above fiber saturation (e.g., 28%
moisture content for plywood). Above fiber saturation, wood decay can occur. However, the wood
must be warm {above 10 °C (50 °F) and optimally between 24 °C (75 °F) and 32 °C (90 °F)}
(Sherwood 1994). Concerns regarding the possibility of decay tend to be worse in manufactured
houses because they tend to have higher indoor relative humidity compared to site-built houses. This
is because they are tighter (Hadley and Bailey 1990) and have smaller interior volumes than site-built
houses.
In an effort to prevent roof cavity moisture problems, the Department of Housing and Urban
Development (HUD) issued rules in their Manufactured Home Construction and Safety Standards
(U.S. Department of Housing and Urban Development 1994). Henceforth in this report, these
standards will be referred to as the HUD Standards. The rules require manufactured houses to have
an interior ceiling vapor retarder, except for houses constructed in the southeastern part of the United
States where a ceiling vapor retarder is optional. In addition, houses constructed with moisture
absorbing roof sheathing are required to be provided with either a passive or mechanical attic
ventilation for removing moisture from their roof cavities. Passive attic ventilation systems shall
have a net free ventilation opening of 1/300 of the attic floor area. Mechanical attic ventilation
systems shall provide a minimum air change rate of 0.00010 m3/s per m2 (0.02 ft3/min per ft2) of attic
floor area. Single-wide houses constructed with metal roofs are not required to have attic ventilation.
Providing an interior vapor retarder in the ceiling construction and ventilating the roof cavity may
be counter-productive and actually cause a summer moisture problem in manufactured houses
located in hot and humid climates. This is because the attic ventilation airflow transports a large
amount of moisture into the roof cavity from the outdoors. This moisture subsequently diffuses
downward through the insulation to the upper surface of the vapor retarder which may be cooled by
the indoor air conditioning equipment below the dew point temperature of the roof cavity air. In this
situation, condensation occurs and the relative humidity at the upper surface of the vapor retarder
approaches a saturated state, thereby providing a conducive environment for mold and mildew
growth. A monthly mean surface relative humidity greater than 80% is conducive to mold and
1
In this report, the attic of a manufactured house is referred to as a “roof cavity” in order to emphasize
that it generally has a smaller volume with less ventilation clearance than a site-built house.
2
mildew growth (International Energy Agency 1990). Once mold and mildew exists, fungal spores
may enter the living space and cause indoor air quality and health-related problems (Olson, J.,
Schooler, S., and Mansfield, M. 1993).
A transient heat and moisture transfer model (Burch and Thomas 1991), developed at the National
Institute of Standards and Technology (NIST) and called MOIST, was recently used to analyze the
effectiveness of various moisture control practices for the roof cavities of manufactured housing. In
that previous study (Burch 1995), it was found that a combination of passive measures consisting
of a ceiling vapor retarder, sealing air leakage sites in the ceiling construction, and providing attic
ventilation openings maintained the moisture content of the roof sheathing well below fiber
saturation. However, the version (2.1) of the MOIST model used in that study had several important
limitations that likely influenced the results. First, the indoor relative humidity in the house below
had to be held constant during the simulation. In actual houses, the indoor relative humidity varies
considerably throughout the year and that can influence moisture content results substantially
(Tsongas, Burch, Roos, and Cunningham 1995). Second, the stack effect airflow from the house into
the roof cavity was treated as constant. In practice, this airflow will tend to vary with the time of
year. And third, the attic ventilation rate was taken to be constant during the simulation. In practice,
the attic ventilation rate varies as a function of the outdoor wind speed.
Because of the above limitations, it was decided to modify the model to remove the limitations. In
the present study, a more comprehensive model is presented that allows analysis without the above
limitations. The model is used to simulate the performance of a current practice double-wide
manufactured house. Various factors that affect the moisture content of the roof sheathing are
analyzed. The effectiveness of the current moisture control practices specified within the HUD
Standards are investigated in several cold climates and a hot and humid climate.
THEORY
Assumptions
Some of the more important assumptions of the new roof cavity moisture and heat transfer model
are given below:
Moisture and heat transfer are one-dimensional;
Air within the ventilated cavity is well mixed; and
The wetting of exterior surfaces by rain is neglected, and the insulating
effect and change in roof absorptance from a snow load are neglected.
Other assumptions are discussed in the model presentation below.
3
Basic Transport Equations
The basic transport equations are taken from Pedersen (1990) and are briefly presented below.
Within each material of the construction, the moisture distribution is governed by the following
conservation of mass equation:
Symbols are defined in the Nomenclature at the end of the report. The first term on the left side of
Equation 1 represents water-vapor diffusion, whereas the second term represents capillary transfer.
The right side of Equation 1 represents moisture storage within the material. The minus sign
accounts for the fact that liquid flows in a porous material in the same direction as the gradient in
capillary pressure. The sorption isotherm (i.e., the relationship between equilibrium moisture content
and moisture content) and the capillary pressure curve (i.e., the relationship between capillary
pressure and moisture content) were used as constitutive relations in solving Equation 1.
The temperature distribution is calculated from the following conservation of energy equation:
The first term on the left side of Equation 2 represents conduction, whereas the second term is the
latent heat transfer derived from any phase change associated with the movement of moisture. The
right side of Equation 2 represents the storage of heat within a material.
In Equation 1, the water vapor permeability (µ) and the hydraulic conductivity (K) are strong
functions of moisture content. In Equation 2, the thermal conductivity (k) is also a function of
moisture content, but for the present analysis it is assumed to be constant.
Ventilated Cavity Moisture and Heat Balance
Applying the principle of conservation of mass to a ventilated cavity, the sum of the evaporation rate
from the ventilated cavity surfaces plus the rate of moisture transfer by airflow from the house into
the cavity is equal to the rate of moisture removed by outdoor ventilation, or:
4
In a similar fashion, the principal of conservation of energy may be applied to the cavity air volume.
The net rate of convective heat transfer from the cavity surfaces plus the rate of energy transfer by
airflow from the house into the cavity is equal to the rate of energy removed by outdoor ventilation,
or:
Radiation exchange among the ventilated cavity surfaces is handled using the mean-radianttemperature network method described by Carrol (1980).
Airflow from House into Attic
The airflow rate from the house into the roof cavity is predicted using the equation (ASHRAE 1993):
Airflow passes through the following three leakage areas: the ceiling, the roof, and the house below.
The effective leakage area of the series combination of the three areas is given by the relation:
Here the effective leakage area for each of the house parts has been aggregated at a single location
placed at the mid-height level of each part. The total stack-effect pressure head ( pt) is equal to the
sum of the pressures for the house and the roof cavity, or:
The first and second terms are the house and roof cavity stack effect pressures, respectively.
5
The NIST Contaminant Air Flow Model (Walton 1994) was used to investigate the validity of the
assumption of aggregating the wall effective leakage area (ELA) at a single location at the midheight level. For the investigation, the stack-effect airflow from the house into the roof cavity was
predicted for two cases. In the first case, the wall ELA was equally distributed into eight separate
ELA’s spaced at equal intervals from the floor to the ceiling. In the second case, the wall ELA was
aggregated at a single location at the mid-height level. The two simulations agreed within 9%,
thereby supporting the validity of the simplifying assumption.
Roof Cavity Ventilation Rate
The single-zone infiltration model developed by Sherman and Grimsrud (1980) was applied to
estimate the air exchange rate between a roof cavity and the outdoor environment, or:
The coefficients (C T,c and Cv,c) were evaluated by fitting the above equation to a set of measured
data, as described in a later section.
Indoor Boundary Conditions
At the indoor surface of the construction, the moisture transfer through an air film and paint layer
(or wallpaper) is equated to the diffusion transfer into the solid material surface, or:
where the quantities are evaluated at the indoor surface. Here, an effective conductance (Me,i),
defined by:
has been introduced. The effect of a thin paint layer is taken into account as a surface conductance
(Mp,i) in series with the convective mass transfer coefficient (Mf,i) associated with the air film.
6
At the same boundary, the heat transferred through the air film, ignoring the thermal resistance of
the paint layer, is equated to the heat conducted into the indoor surface, giving:
where all quantities are evaluated at the indoor surface.
Outdoor Boundary Conditions
At the outdoor surface of the construction, a set of equations similar to Equations 9 and 10 were
applied to compute the moisture transfer. The heat conducted into the outdoor surface and the
absorbed solar radiation is set equal to the heat loss to the outdoor air by convection and thermal
radiation between the surface and sky, or:
where all quantities are evaluated at the outdoor surface. Here hr,o is the radiative heat transfer
coefficient defined by the relation:
where E is the emittance factor which includes the surface emissivity and the view factor from the
outdoor surface to the sky and Tm is the mean temperature between the surface and the sky. The solar
radiation (Hsol) incident onto exterior surfaces having arbitrary tilt and orientation was predicted
using algorithms given in Duffie and Beckman (1991). The sky temperature was calculated using
an equation developed by Bliss (1961).
Indoor Temperature and Humidity Conditions
Space Heating Operation. When the daily average outdoor temperature is less than or equal to the
balance point temperature for space heating, the house operates in a space heating mode. The indoor
temperature is taken to be equal to the heating set point temperature. The indoor relative humidity
is permitted to vary and is calculated from a moisture balance of the whole building.
7
The rate of moisture production by the occupants is equal to the rate of moisture removed by natural
and /or forced ventilation plus the rate of moisture storage at interior surfaces and furnishings, or:
The sorption constant per unit floor area ( ) must be determined from a whole house experiment (see
TenWolde 1994). Using the psychrometric relationship between humidity ratio ( ) and relative
humidity ( ) as a constitutive relation, the above equation may be solved for the indoor relative
humidity.
The hygric memory (
i,
) is computed from the relation:
The exponential weighting factors Z(n) are defined as:
In the hourly calculations, the dew point temperature of the indoor air is compared with the
temperature of the inside glass surface to determine if condensation occurs. When condensation
occurs, the vapor pressure of the indoor air is taken to be equal to the saturation pressure at the inside
glass surface. The indoor relative humidity is calculated from the indoor temperature and vapor
pressure using psychrometric relationships.
The natural ventilation rate for the house is predicted by the single-zone Lawrence Berkeley
Laboratory (LBL) Infiltration Model developed by Sherman and Grimsrud (1980) and described by
ASHRAE (1993) which is given by:
8
When mechanical ventilation Vh,m is present, the total ventilation rate Vh,t in Equation (14) is
determined by the relation (Palmiter and Bond 1991):
It should be noted that in Equation 18, Vh,m is the actual mechanical ventilation rate produced by the
ventilation equipment installed in the house, as opposed to the rated value. The actual value is
typically about half of the rated value (Tsongas 1990).
Space Cooling Operation. When the daily average outdoor temperature is greater than or equal to
the balance point temperature for space cooling, the house operates in a space cooling mode. The
indoor temperature and relative humidity are maintained at constant specified values.
Floating Operation. When the daily average outdoor temperature is greater than the balance point
for space heating and less than the balance point for space cooling, then neither space heating nor
space cooling are required, it is assumed that the windows are opened, and the indoor temperature
and relative humidity are equal to the outdoor values. When the space cooling equipment is turned
off, it was assumed that the occupant will open the windows, and the building again operates in a
well ventilated mode.
Solution Procedure
A FORTRAN 77 computer program, called the MOIST Attic Model, was prepared to solve the
above system of equations. Finite-difference equations were developed to represent the basic
moisture and heat transport equations (Eqs. 1 and 2).
The solution of the complete system of equations proceeded by first solving for the all material
temperatures and the cavity air temperature. A flow chart describing the steps of the thermal solution
is given in Figure 1. Since the material temperatures and the cavity air temperature are dependent
upon one another, it is necessary to iteratively solve at each time step the material temperatures and
cavity air temperature until convergence is achieved.
The model next solves for the water vapor pressure distribution within the materials and the cavity
water vapor pressure. A flow chart describing the steps of the moisture solution is given in Figure 2.
Since the material vapor pressures and the cavity vapor pressure are dependent on one another, it is
necessary to iteratively solve at each time step the material vapor pressures and cavity vapor pressure
until convergence is attained. The model next solves for the distribution of capillary pressures within
the materials. From the predicted gradients in vapor pressure and capillary pressure and the transport
coefficients for vapor and liquid flows, a new set of material moisture contents is calculated. The
model is now ready to proceed to the next time step.
9
Before making the final computer runs for the present study, a series of special computer runs were
carried out to establish that the finite-difference representation of the transport equations was indeed
converging. In a sequence of simulations, the number of the finite-difference nodes in each material
was doubled until no further change in the solution occurred.
The number of finite-difference nodes used in the roof construction, which is the focus of the
analysis, is given in Table 1 below.
Table 1. Number of Finite-Difference Nodes in Roof Construction
Construction Layer
Thickness, mm (in.)
Nodes
Thin Surface Layer, Plywood Roof Sheath
1.3 (0.050)
2
Remainder Layer, Plywood Roof Sheath
10.6 (0.419)
5
Building Paper
0.79 (0.031)
2
6.4 (0.25)
2
Asphalt Roof Shingles
Dividing the plywood into two separate layers (i.e., a thin surface layer and a remainder layer) is a
trick used to achieve convergence of the mathematical solution with a fewer number of nodes. This
also allowed determination of the moisture content of the plywood sheathing adjacent to the cavity.
A similar number of nodes were used in the other construction components. The thin surface layer
should have the highest moisture content of the sheathing.
In another set of simulations, the convergence criteria for the thermal solution ( T) and the
convergence criteria for the moisture solution ( M) were decreased until no further change in the
solution occurred. A value of 1.0 X 10-4 for m and T provided convergence of the mathematical
solution.
DESCRIPTION OF CURRENT PRACTICE HOUSE
In selecting the construction of the current practice house, the authors contacted manufacturers and
other persons knowledgeable of manufactured home construction. An effort was made to select
construction characteristics representative of current construction practice.
The house simulated in this study was a double-wide manufactured house having a floor area of
130.3 m2 (1402 ft2) and a 2.44 m (8 ft) ceiling height. The size of the house was based on a control
group of 29 manufactured houses studied by Palmiter, Bond, Brown, and Baylon (1992).
A cross section of the roof construction is shown in Figure 3. The sloping roofs faced north and
south; the gable end walls faced east and west. The slope of the roof was 14°. The roof construction
was comprised of 12 mm (15/32 in.) exterior-grade plywood, asphalt roofing paper, and asphalt
shingles. The shingles were medium-dark colored and had a solar absorptance of 0.8. The gable end
12
walls were constructed of 9.5 mm (3/8 in.) asphalt-impregnated fiberboard and vinyl siding. The
ceiling construction (or floor of the roof cavity) consisted of 180 mm (7.1 in.) [R-3.9 m2@K/W (R-22
h@ft2@° F/Btu)] glass-fiber insulation, 0.15 mm (6 mil) kraft paper vapor retarder, and 13 mm (0.5 in.)
gypsum board with 575 ng/s@m2@Pa (10.0 perm) latex paint applied to its interior surface.
In the roof and ceiling construction, the framing members (including trusses) were spaced 0.41 m
(16 in.) on center.
Based on the control group of 29 houses studied by Palmiter, Bond, Brown, and Baylon (1992), the
whole house was assumed to have an effective leakage area (ELA) of 594 cm2 (92 in.2 ).2 Based on
airtightness test results of twenty site-built houses (Buchan, Lawton, Parent Ltd 1991), the authors
assumed that the ceiling ELA was 35% of the whole house total or 206 cm2 (32 in.2 ). The ELA for
the house below (excluding the ceiling and roof construction ) was 65% of the whole house total or
387 cm2 (60 in.2 ).
Consistent with the current HUD Standards for manufactured housing, the gable end walls and the
roof construction were fitted with roof cavity vents having a net free open area of 1/300 of the floor
area or 4,340 cm2 (673 in.2). When computer simulations were conducted in a current practice house
without roof cavity vents, the authors assumed that unintentional air leakage sites in the construction
provided a leakage area of one-tenth that provided by the roof cavity vents themselves or 434 cm2
(67.3 in.2).
Consistent with the HUD Standards, the current practice house was provided with indoor mechanical
ventilation having an average air change rate of 0.00018 m3/s per m2 (0.035 ft3/min per ft2) of floor
area or 0.023 m3/s (49 ft3/min).
PARAMETERS USED IN ANALYSIS
Water Vapor Diffusion Properties
Sorption Isotherms. For most of the hygroscopic materials comprising the roof construction of the
current practice house, sorption isotherms were measured in the laboratory at the National Institute
of Standards and Technology. A sorption isotherm is the relationship between moisture content and
relative humidity at equilibrium. The sorption isotherms were determined by placing eight small
specimens of each material in vessels above saturated salt-in-water solutions. Each saturated salt-inwater solution provided a fixed relative humidity (Greenspan 1977). The vessels were maintained
at a temperature of 24 °C ± 0.2 °C (75 °F ± 0.4 °F) until the specimens reached a steady-state
equilibrium. The equilibrium moisture content was plotted versus relative humidity to give the
sorption isotherm. Separate sorption isotherm data were obtained for specimens initially dry
Under a temperature difference of 16.7 EC (30.0 EF) and a 4.9 m/s (11 mph) wind speed, a
house ELA=594 cm2 (92 in.2) provides a natural house infiltration rate of approximately 0.48 air
changes per hour (based on Equation 17).
2
14
(adsorption isotherm) and for specimens initially saturated (desorption isotherm). A detailed
description of the measurement method is given in Richards et al. (1992).
Edwards (1996) and Hedlin (1967) have studied the effect of temperature on the sorption isotherm
for a few building materials and found the effect to be small. For the present analysis, the effect of
temperature on the sorption isotherm was neglected.
The mean of the adsorption and desorption isotherm measurements was fit to an equation of the
following form:
The coefficients B1, B2, and B3 were determined by regression analysis and are summarized in Table
2. A plot of the sorption isotherms of the materials is given in Figure 4. The asphalt roof shingles
and vinyl siding were treated as vapor impermeable materials, and the storage of moisture in these
materials was neglected.
The uncertainty in the sorption isotherm measurements was within ± 1.5% moisture content.
Table 2. Sorption Isotherm Regression Coefficients
Materials
B1
B2
B3
Exterior-Grade Plywood Sheathing
0.344
6.18
0.828
Sugar Pine
Framing and Truss Members
0.192
2.05
0.765
0.001703
0.0
0.963
51.9
2538.
.902
0.00336
0.0
.901
Asphalt-Impreg. Fiberboard
1.14
50.6
0.923
Asphalt Roofing Paper1
51.9
2538.
0.902
Glass-Fiber Insulation
Kraft Paper
Gypsum Board
1
The regression coefficients for asphalt roofing paper were assumed to be the same as for kraft paper. Since
this material is very thin, moisture storage in this material will have very little effect on the predicted
moisture content of the plywood roof sheathing. Therefore, the assumed property value may be used in the
analysis.
Permeability Measurements. The water-vapor permeability of most of the hygroscopic materials was
measured using permeability cups placed in controlled environments. Five circular specimens, 140
mm (5.5 in.) in diameter, of each material were sealed at the top of open-mouth glass cups. The cups
were subsequently placed inside sealed glass vessels maintained at a constant temperature. Saturated
salt-in-water solutions were used inside the glass cups and surrounding glass vessels to generate a
15
relative humidity difference of approximately 10% across each specimen. By using different salt
solutions, the mean relative humidities across the specimens were varied over the humidity range
of 11% to 97%. Permeability was plotted versus the mean relative humidity across the specimens.
Separate measurements conducted at 7 EC (45 °F) and 24 °C (75 °F) revealed that temperature has
a small effect on permeability over this particular temperature range. A detailed description of the
permeability measurement method is given in Burch et al. (1992).
Water vapor permeability data were plotted versus the mean relative humidity across the specimen
and fit to an equation of the form:
Here the permeability (µ) is expressed in ng/s@m@Pa. The coefficients C1, C2, and C3 were determined
by regression analysis and are summarized in Table 3. A plot of the permeance (i.e., permeability
divided by thickness) of the materials is given in Figure 5. The asphalt roof shingles and vinyl siding
were treated as vapor impermeable materials.
The uncertainty in measuring the permeability of the materials was less than 5% when measuring
materials having a permeance less than 575 ng/s@m2@Pa (10 perm). However, the uncertainty
increased rapidly as the specimen permeance rose above 575 ng/s@m2@Pa (10 perm).
The mass transfer coefficients for the boundary air layers in contact with surfaces of the roof cavity
were predicted using the Lewis relationship between heat and mass transfer (Threlkeld 1970). The
permeance of the latex paint was assumed to be 575 ng/s@ m2@Pa (10 perms).
Liquid Diffusivity
In a few of the simulations, the moisture content in the plywood roof sheathing and the wood
framing members rose above fiber saturation during the winter. Liquid water coalesced within the
“large” pores of the materials. Under this condition, capillary transfer occurred, and liquid diffusivity
is the fundamental moisture transport coefficient. The hydraulic conductivity (K) in Equation (1) is
related to the liquid diffusivity (D ) by the relation:
17
Table 3. Permeability Regression Coefficients
Materials
C1
C2
C3
Exterior-Grade Plywood Sheathing
0.806
0.00163
9.765
Sugar Pine
Framing and Truss Members
0.442
0.000910
9.86
182
0.0
0.0
0.00626
0.000896
4.01
Gypsum Board
63.8
0.0
0.0
Asphalt-Impreg. Fiberboard
34.4
0.0
0.0
Asphalt Roofing Paper2
0.511
0.0.
0.0
Glass-Fiber Insulation1
Kraft Paper
1
The permeability of glass-fiber insulation was assumed to be equal to the permeability of a stagnant air
layer. This assumption is reasonable because the glass fibers of the insulation occupy a small fraction of its
volume. Bound-water diffusion along the glass fibers is small compared with molecular diffusion through
the predominantly open pore space.
2
Based on data contained in ASHRAE (1993).
where the term in the dominator of the right side of the equation is the derivative of the capillary
pressure with respect to moisture content.
For the plywood roof sheathing, the authors used liquid diffusivity measurements for grooved
exterior-grade plywood (Richards 1992). For the framing members, the authors used liquid
diffusivity measurements for sugar pine (Richards 1992). The authors believe that they were justified
in using liquid diffusivity measurements of similar materials for the following reasons. In most of
the computer simulations, the materials operated entirely in the hygroscopic regime and the capillary
coefficients were never used in the calculations. In the remainder of the computer simulations, the
material operated predominantly in the hygroscopic regime and moved into the capillary regime only
during brief periods, except for two worst case houses (i.e., very high indoor relative humidity
without attic ventilation). Moreover, the capillary transfer coefficient does not govern how much
moisture reaches the plywood layer, but rather the re-distribution of moisture across the thickness
of the plywood layer. Very little liquid water is transferred to the adjacent building paper because
the building paper offers high resistance to capillary flow.
19
Airflows
Roof Cavity Ventilation Rate. Buchan, Lawton, Parent Ltd (1991) measured sixty attic ventilation
rates in twenty houses in several Canadian climates. The houses had different types of attic
ventilation with a wide range of ELA’s measured using a pressurization technique. For each of the
measurements, they also measured the wind speed, wind direction, and temperature difference
between the roof cavity and the outdoor environment. The authors applied Equation 8 to this set of
data and used regression analysis to determine the empirical coefficients. The stack coefficient (C T,c)
was determined to be a very small value and was taken to be zero. The wind coefficient (CV,c) was
found to be 6.94 x 10-5 (L/s)2@(cm)-4@(m/s)-2 [0.00259 [email protected]@mph-2].
A plot of the volumetric attic ventilation rate per unit roof effective leakage area as a function of
wind speed is given in Figure 6. Each point represents one of the measurements of Buchan, Lawton,
Parent Ltd (1991). The least-squares-fit correlation is also given in the plot of Figure 6. It should be
noted that a great deal of scatter exists between the least-squares-fit correlation and the measurement
points. A contributing factor is that the least-squares-fit correlation does not include wind direction
and attic ventilation type. Upper and lower bounds for the measured data are also shown on the plot.
With the exception of a few points deemed to be outliers, most of individual measurements fall
between the upper and lower bounds.
House Natural Ventilation Rate. For the semi-empirical relation (Equation 17), the stack coefficient
(C T,h) was taken to be the ASHRAE (1993) value 0.000145 (L/s)2@cm-4@°C-1 [0.0156 [email protected]@°F-1]
for a one-story house. The wind speed coefficient (CV,h) was taken to be the ASHRAE (1993) value
0.000104 (L/s)2@(cm)-4@(m/s)-2 [0.0039 [email protected]@mph-2] for a one-story house with a shielding class
of 4.
Heat
The thermal conductivity, density, and specific heat of the materials were taken from ASHRAE
(1993).
Other Properties
The long-wave emittance of the materials was taken to be 0.9. The solar absorptances of the asphalt
roofing shingles and the vinyl siding applied to the gable end walls were taken to be 0.8 and 0.6,
respectively. The 0.8 absorptivity value is the mean value measured by Parker, et al. (1993) for
thirty-four different colored asphalt roof shingles.
Indoor and Outdoor Conditions
In the computer analysis, the hourly outdoor boundary conditions (i.e., ambient temperature, relative
humidity, wind speed, and incident solar radiation) were obtained from ASHRAE WYEC weather
data (Crow 1981). During the winter when space heating was required, the set point temperature was
20
20 °C (68 °F). The occupant activities produced moisture at a rate of 10.9 kg/day (24.0 lb/day) unless
stated otherwise, and the indoor relative humidity during the winter was predicted from a moisture
balance of the whole building. During the summer when space cooling was required, the set point
temperature and indoor relative humidity were 24 °C (76 °F) and 56%, respectively.
Six months of weather data were used to initialize the reported one-year simulation results in order
to reduce the effect of assumed initial construction layer moisture content and temperature. The
moisture performance of the prototype roof was analyzed for the cold climates of Madison, WI (most
simulations); Boston, MA; Portland, OR; and Atlanta, GA; as well as the hot and humid climate of
Miami, FL.
COLD CLIMATE RESULTS
Performance of Current-Practice House in Madison
The new attic model was first used to predict the weekly average moisture content of the roof cavity
surfaces for the current-practice house located in Madison, WI. The surface moisture contents are
plotted versus time of year in Figure 7. The moisture content of the roof rafters (not shown) tended
to track the plywood roof sheathing but were slightly lower. The surface moisture contents are lowest
during summer and rise to a maximum during fall and winter. The construction component having
the highest surface moisture content is the north sloping plywood roof. The peak plywood moisture
content is seen to be 16% (dry mass basis), and is well below fiber saturation (i.e., a moisture content
of 28%). It should be pointed out that the moisture control practices (i.e., installing an interior ceiling
vapor retarder and providing passive roof cavity vents consistent with the 1/300 rule) are
implemented on this house. The volumetric attic ventilation rate was predicted using the leastsquares-fit correlation (see Figure 6).
The model was next used to investigate the relative importance of various parameters on the roof
cavity performance. The approach was to vary one parameter at a time and investigate its effect on
the moisture content of the north sloping plywood roof. Henceforth in this report, the winter analysis
will focus on the moisture content of the north sloping plywood roof, since this construction
component always had the highest moisture content. Unless stated otherwise, the climate is Madison,
WI.
Effect of Roof Cavity Ventilation
Passive Roof Cavity Ventilation. The model was next used to investigate the consequences of not
providing any roof cavity vents. When the ventilation openings were not present, it was assumed that
unintentional air leakage sites in other parts of the construction provided an ELA of 434 cm2 (67.3
in.2 ) which was one-tenth of that provided by the passive ventilation openings themselves. Figure
8 compares the north sloping roof moisture content of two identical current-practice houses, one with
and the other without roof cavity vents. When roof cavity vents were provided, their ELA was set
equal to the net free open area specified by the 1/300 rule. In the house without roof cavity vents
22
(upper curve), the moisture content rises almost to fiber saturation (depicted by the horizontal line
at 28% moisture content). On the other hand, in the house with roof cavity vents (lower curve), the
moisture content is maintained well below fiber saturation. These results demonstrate that
appropriately sized roof cavity vents are very effective in removing moisture and maintaining the
roof sheathing moisture content at acceptable levels.
Mechanical Roof Cavity Ventilation. The model was next used to investigate the effectiveness of
the specified mechanical ventilation rate in the HUD Standards that permits mechanical ventilation
to be substituted for passive roof cavity vents. The HUD Standards specify that the mechanical
ventilation rate shall be at least 0.00010 m3/s per m2 (0.02 ft3/min per ft2) of attic floor. The current
practice house has a floor area of 130 m2 (1402 ft2), and the mechanical ventilation rate is calculated
to be 0.013 m3/s (28 ft3/min). The results of a computer simulation with the roof cavity ventilated
at this constant rate are shown in Figure 9. Note that the predicted moisture content of the plywood
roof sheathing (upper curve) rises to fiber saturation during the winter. These results indicate that
the mechanical attic ventilation rate specified in the HUD Standards is too low under some
conditions and needs to be increased to achieve acceptable performance. This is especially critical
since some houses will have greater moisture flow into the attic than assumed in this analysis.
The previous results with passive roof cavity vents provided satisfactory performance (see Figure
8). An effort was made to find a mechanical ventilation rate that would provide the same amount of
attic ventilation as the passive ventilation openings operated under prevailing outdoor wind speeds.
From the Climatic Atlas of the United States (1983), the mean January wind speed for many parts
of the United States is approximately 4.9 m/s (11 mph). From Equation 8, an equivalent mechanical
ventilation rate of 0.175 m3/s (370 ft3/min) was determined.
A computer simulation was carried out using the above equivalent mechanical ventilation rate of
0.175 m3/s (370 ft3/min). In addition, simulations were conducted at attic mechanical ventilation
rates of 0.123 m3/s (260 ft3/min) and 0.068 m3/s (144 ft3/min). The results are included in Figure 9.
Notice that all of the above revised mechanical ventilation rates had roof sheathing moisture contents
that were well below fiber saturation. Based on these results, it is recommended that the prescribed
mechanical attic ventilation rate be the lower of the revised rates or 0.068 m3/s (144 ft3/min).
Expressing this figure on a per unit attic floor area, the specified mechanical attic ventilation rate
should be 0.0005 m3/s per m2 (0.1 ft3/min per ft2).
Effect of a Ceiling Vapor Retarder
The model was next used to investigate the effect of a ceiling vapor retarder. Separate computer
simulations were carried out with and without a ceiling vapor retarder. The results are given in
Figure 10a for a house with roof cavity vents and in Figure 10b for a house without roof cavity vents.
The presence of the vapor retarder has a small effect on the roof sheathing moisture content. This
is because water vapor diffusion is transporting much less moisture than airflow from the house into
the roof cavity as shown in the next section. A ceiling vapor retarder had a small effect because
airflow from the house into the roof cavity was the dominant moisture transport mechanism.
25
Effect of Airflow from House into Roof Cavity
A simulation was next conducted of the current practice house with the ceiling ELA reduced to zero,
thereby eliminating airflow from the house into the roof cavity. The current practice house without
airflow (lower curve) is compared to the same house with a representative airflow in Figure 11.
Representative airflow was achieved by using a wall ELA of 387 cm2 (60 in.2 ), a ceiling ELA of 206
cm2 (32 in.2 ), and a roof ELA of 4,340 cm2 (673 in.2 ) in the stack-effect airflow equations. Here the
roof ELA is set equal to the net free opening specified by the 1/300 rule.3 When the ceiling airflow
is zero, the roof sheathing moisture content is lower. Comparing these results to the previous results
of Figure 10, airflow is seen to have a larger impact on the roof sheathing moisture content than
water vapor diffusion.
Effect of Indoor Relative Humidity
In this section, the effect of indoor relative humidity on the roof sheathing moisture content is
analyzed.
Humidified Houses. The current practice house was simulated with a humidifier that maintained a
constant indoor relative humidity of 45% during the winter. An indoor relative humidity of 45% is
the highest humidity that can be maintained without condensation on double-pane windows. The
roof sheathing moisture content of the humidified house is compared to the same house without
humidification in Figure 12a. In the humidified house (upper curve), the moisture content of the
north sloping plywood roof sheathing rose to a peak of 25% and approached fiber saturation (28%).
Note, however, that both roofs dry out quickly in the spring. Here the rate of moisture transport from
the house into the roof cavity is approaching the limit of effective removal by passive attic
ventilation. The large difference in roof sheathing moisture content between the humidified and nonhumidified house is a direct consequence of the indoor relative humidity difference between the two
houses depicted in Figure 12b.
Non-Humidified Houses. A number of factors affect the indoor relative humidity in non-humidified
houses, including the indoor moisture production rate, the house ELA, and indoor mechanical
ventilation, when it is present.
Separate computer simulations of the current practice house were conducted with the following
moisture production rates: high: 16.3 kg/day (36 lb/day), typical: 10.9 kg/day (24 lb/day), and low:
5.4 kg/day (12/day). The resulting plywood moisture contents and indoor relative humidities are
shown in Figures 13a and 13b, respectively. As the moisture production rate increases, the peak
plywood moisture content is seen to rise in response.
3
In a strict sense, effective leakage area is somewhat different than net free area due to airflow
entrance effects.
28
Several simulations of the current practice house were conducted with the following three house
ELA’s: a leakier house: ELA=787 cm2 (122 in.2 ), a typical house: ELA=594 cm2 (92 in.2 ), and a
tighter house: ELA=400 cm2 (62 in.2 ). In these simulations, the ceiling ELA was maintained at a
constant value of 206 cm2 (32 in.2 ). Here the authors assumed that ceiling air leakage through
partition walls, ceiling light fixtures, plumbing and HVAC penetrations would remain constant as
the exterior wall ELA was varied. These three simulation are shown in Figure 14. As the house
becomes tighter, less natural infiltration occurs, and the indoor relative humidity rises. This causes
the roof sheathing moisture content to slightly increase during the fall and winter.
Several simulations were also conducted with the following three levels of continuous indoor
mechanical ventilation: none, the current practice house at a typical rate of 0.023 m3/s (49 ft3/min),
and at a very high rate of 0.071 m3/s (150 ft3/min). These ventilation rates are actual values, as
opposed to rated values. The high ventilation rate corresponds to continuous operation of the kitchen
and bathroom ventilation exhaust fans or a large exhaust only whole house ventilation system. The
typical rate is the ventilation rate currently specified by the HUD Standards. Predicted roof sheathing
moisture contents for the three cases are given in Figure 15. The results indicate that indoor
mechanical ventilation slightly decreases the moisture content of the roof sheathing due to reductions
in indoor relative humidity. The results of Figure 15 also indicate that, if the homeowner were to
modify the HVAC equipment and turn off the continuous ventilation specified in the HUD
Standards, then the roof sheathing moisture content would increase by only approximately 2%, but
moisture levels are still below fiber saturation (28%).
Effect of Outdoor Climate
The model was next used to simulate the current practice house in the following four winter
climates: a very cold climate (Madison, WI ), a moderately cold climate (Boston, MA), a mild
climate (Atlanta, GA), and cool Pacific northwest climate (Portland, OR). The roof sheathing
moisture content and indoor relative humidity values are depicted in Figure 16a and 16b,
respectively. These results show a considerably smaller sensitivity to climate compared with
previous results (Burch 1995) in which the indoor relative humidity was maintained constant during
the simulation. The present results with variable indoor relative humidity show less climatic
sensitivity because the indoor relative humidity is lower in cold climates during the winter months
(see Figure 16b). This diminishes the vapor pressure potential for the moisture transport. On the
other hand, milder climates tend to have higher indoor relative humidities during winter months, but
there is less opportunity for condensation. The small effect of climate on winter moisture
accumulation has also been reported to occur in walls when the indoor relative humidity is permitted
to vary during the winter rather than being held constant (Tsongas, Burch, Roos, and Cunningham
1995).
32
Other Factors
The model was used to simulate the current practice house with the following four winter set point
temperatures: 17.2 °C (63 °F), 20.0 °C (68° F), 22.8 °C (73 °F), and 25.6 °C (78 °F). The results,
plotted in Figure 17a, reveal that slightly more moisture accumulates in the roof sheathing of colder
houses.
The current practice house was next simulated with sky radiation turned off in the model. This result
is compared to the same house with sky radiation in Figure 17b. This comparison indicates that the
roof sheathing moisture content is about 4% mc higher when sky radiation is included in the analysis.
This is because thermal radiation to the sky significantly reduces the roof sheathing temperature, and
thereby increases the roof sheathing moisture content.
The current practice house was simulated with a light colored roof (solar absorptance = 0.65), a
medium colored roof (solar absorptance = 0.8), and a dark colored roof (solar absorptance = 0.95).
The results given in Figure 17c reveal that dark colored roofs have a slighter lower roof sheathing
moisture content. This is because they absorb more solar energy and operate at a higher temperature
and thereby decrease the roof sheathing moisture content.
A simulation of the current practice house was also conducted without the interior wood trusses.
When this result was plotted (not shown) and compared to the same house with the interior wood
trusses, both results were observed to be almost identical, thereby indicating that wood trusses play
an insignificant role in the moisture performance of ventilated roof cavities.
Summary of Effect of Parameters
The effect of the various parameters on the moisture content of the roof sheathing is summarized in
Table 4. The difference in moisture content presented in the last column is the maximum estimated
difference in moisture content observed at the peak roof sheathing moisture content.
From Table 4, attic ventilation (both passive and mechanical) and indoor humidification are seen to
affect the roof sheathing moisture content by more than 12% mc. The effect of outdoor climate, sky
temperature, and indoor moisture generation rates are somewhat less, ranging between 4-7% mc. The
effects of the other parameters are each less than 3% mc.
PROVIDING WHOLE HOUSE VENTILATION WITH CEILING VENTS
It is possible to provide whole house ventilation by installing several ventilation openings in the
ceiling of a manufactured house. Ceiling vents will increase the airflow from the house into the attic
and thereby reduce the indoor relative humidity. However, increased airflow will transport more
moisture into a roof cavity and increase the space heating load as shown below.
36
Table 4. Effect of Parameters on Roof Sheathing Moisture Content1
Parameter
Diff. (% mc)
Passive Attic Ventilation (Roof Cavity Vents vs. None)
12
Mechanical Attic Ventilation (Wide Range)
13
Ceiling Vapor Retarder (with vs. without)
* with Roof Cavity Vents
* without Roof Cavity Vents
1
3
Ceiling ELA with Passive Ventilation (Typical vs. None)
2
Indoor Humidification (with vs. without)
14
Indoor Moisture Generation Rate (Low vs. High)
5
Whole House ELA (Leakier vs. Tighter House)
2
Indoor Mechanical Ventilation (High vs. None)
3
Outdoor Climate Band
7
Indoor Temperature (Typical Range)
2
Sky Temperature (with vs. without)
4
Roof Color (Solar Absorptance Range: 0.65 to 0.95)
2
1
The current practice house with a ceiling vapor retarder and 1/300 roof cavity vents was used as
a baseline.
Two computer simulations of the current practice house were conducted with two ceiling vent
openings each having an ELA of 310 cm2 (48 in.2 ). These two vent openings and the ceiling
construction itself gave a total ceiling ELA of 826 cm2 (128 in.2 ). In the first simulation, it was
assumed that the roof cavity vent openings were sealed. In the second, it was assumed that the roof
cavity contained vent openings consistent with the 1/300 rule. These two simulations are compared
to that of the current practice house in Figure 18.
The roof sheathing moisture content, ceiling airflow rate, and indoor relative humidity for the above
three simulations are given in Figures 18a, 18b, and 18c, respectively. In the house with two ceiling
vents with no roof cavity vents, roof sheathing moisture content rose to 26% and approached fiber
saturation (28%). The presence of the ceiling vents significantly increased the airflow from the house
into the roof cavity (see Figure 18b), thereby transporting more moisture into the roof cavity. The
additional whole house ventilation provided by the ceiling vents also lowered the indoor relative
humidity (Figure 18c), which partially offset the effect of increased house airflow into the attic
(Figure 18b).
38
As pointed out above, the two ceiling vents produced a significant increase in the airflow from the
house into the roof cavity. From Figure 18b, the peak airflow from the house into the roof cavity is
increased from 0.028 m3/s (60 ft3/min) to 0.041 m3/s (86 ft3/min), or a 43% increase. Space heating
energy must be expended to heat additional incoming air. This imposes an annual space heating
energy penalty of 1520 kWh. At 6.4 cents per kWh, the annual cost to the homeowner for this
additional space heating energy will be ninety-seven dollars ($97) in Madison, WI.
When roof cavity vents were added to the house with ceiling vents, the roof sheathing moisture
content decreased approximately back to the level for the current practice house without ceiling vents
(see Figure 18a). In this situation, the roof cavity vents removed a significant portion of the moisture
transported by airflow. Another mitigating factor was that the presence of the roof cavity vents
further increased the whole house ventilation, thereby giving rise to further reductions in indoor
relative humidity (see Figure 18c). However, the roof cavity vents produced a further increase in the
airflow from the house into the roof cavity. This, in turn, further increased the space heating energy
penalty by an additional 810 kWh or fifty-two dollars ($52), giving a total increase of one hundred
forty-nine dollars ($149).
In summary, the practice of providing whole house ventilation by installing ceiling vents without
roof cavity vents has been shown to produce considerably higher roof sheathing moisture contents
that approach fiber saturation. The problem of high sheathing moisture content may be overcome
by installing roof cavity vents consistent with the 1/300 rule. However, the presence of the roof
cavity vents further increased the whole house ventilation, which in turn produced an additional
space heating energy penalty.
EFFECTIVENESS OF MOISTURE CONTROL PRACTICES IN COLD CLIMATES
In this section, the effectiveness of roof cavity vents consistent with the 1/300 rule is investigated
for two worst case indoor relative humidity situations: a tight house having an ELA of 400 cm2 (62
in.2) with a high moisture generation rate of 16.3 kg/day (36 lb/day) and a humidified house. These
situations represent worst-case scenarios, but such extreme conditions are quite likely to exist within
a fraction of the manufactured housing stock. It is crucial that moisture control practices work
satisfactorily in houses operated under worst case humidity conditions. Consistent with the current
HUD Standards, the house had a 57 ng/s@m2@Pa (1 perm) ceiling vapor retarder.
Tight House with High Moisture Generation Rate
Separate computer simulations of this worst case house were carried out for the following levels of
attic ventilation: no roof cavity vents, lower bound roof cavity vents, mean correlation roof cavity
vents, and upper bound roof cavity vents (see Figure 6). The results are given in Figure 19.
40
For all three levels of roof cavity ventilation, the peak roof sheathing moisture content was below
fiber saturation (28%). On the other hand, when no roof cavity vents are provided (upper curve), the
roof sheathing moisture content rose considerably above fiber saturation during the winter and
spring. This high roof sheathing moisture content may pose a risk of material degradation, although
the roof sheathing dries out satisfactorily during warmer spring and summer periods when decay is
more likely to occur.
Humidified House
A similar set of simulations was carried out for a humidified house. The results are given in
Figure 20. When roof cavity vents are not provided (upper curve), moisture accumulated in the roof
sheathing considerably above fiber saturation. Note that the high roof sheathing moisture contents
do not extend significantly into spring and summer periods, when material degradation is likely to
occur. For the three levels of roof cavity ventilation, the mean and upper bound curves were below
fiber saturation, but the lower bound curve rose somewhat above fiber saturation. These results
indicate that some humidified houses with roof cavity vents (consistent with the 1/300 rule) will
experience roof sheathing moisture contents above fiber saturation. Therefore, it is recommended
that manufactured houses not be humidified.
AN ALTERNATIVE ATTIC MOISTURE CONTROL PRACTICE
IN COLD CLIMATES
Instead of providing attic ventilation, some building scientists have advocated sealing air leakage
sites in the ceiling construction. This would reduce the airflow and moisture transport from the house
into the roof cavity, and thereby maintain the roof sheathing moisture content below fiber saturation.
A series of computer simulations was conducted for the above worst case house without roof cavity
vents. In these simulations, the ceiling ELA was varied from zero to 206 cm2 (32 in.2). The results
are depicted in Figure 21. Decreasing the ceiling ELA produced two separate effects. First, it
decreased the airflow from the house into the roof cavity (see Figure 21b). Second, it increased the
indoor relative humidity due to decreased whole house ventilation (see Figure 21c). The two results
had an opposite effect on the roof sheathing moisture content. The overall effect is more gradual than
expected (see Figure 21a). It is not until a ceiling ELA of 26 cm2 (4 in.2) is reached that the roof
sheathing moisture content is decreased sufficiently below fiber saturation. It is questionable whether
such a low ceiling ELA is achievable in houses with roof cavities.
42
EFFECTIVENESS OF CURRENT MOISTURE CONTROL PRACTICES
IN HOT AND HUMID CLIMATES
The model was next used to investigate the attic moisture performance of a current practice house
in a hot and humid climate (Miami, FL). The current HUD Standards require that manufactured
houses distributed in hot and humid climates have their attics ventilated consistent with the 1/300
rule. While a ceiling vapor retarder is not mandatory, it is none-the-less installed in many
manufactured houses distributed to hot and humid climates.
For the current-practice house with a ceiling vapor retarder, separate computer simulations were
carried out for cases with and without roof cavity vents. The results are given in Figure 22a. For both
cases, the surface relative humidity above the ceiling vapor retarder rose above 80% and reached a
peak during the summer. When roof cavity vents were present, the surface relative humidity was
higher and above a relative humidity of 80% for a longer period of time. An explanation is that the
roof cavity vents introduce more moisture (from the humid outdoor air) to the upper surface of the
roof cavity insulation where it readily diffuses to the upper surface of the vapor retarder.
In Figure 22, the horizonal line depicts the critical relative humidity of 80% believed to coincide
with mold and mildew growth. The International Energy Agency (IEA 1990) has published
Guidelines and Practices (Volume 2) for preventing mold and mildew growth at building surfaces.
This consensus document indicates that a monthly mean surface relative humidity above 80% is
conducive to mold and mildew growth. Note that in the computer simulation with a ceiling vapor
retarder and with roof cavity vents, the surface relative humidity rose above the critical 80% relative
humidity for a 4-month summer period.
A similar pair of computer simulations were conducted for the same house without a ceiling vapor
retarder. The results are given in Figure 22b. When roof cavity vents were not present, the roof cavity
performed satisfactorily. That is, the surface relative humidity at the upper surface of the gypsum
board remained below the critical 80% level. In this situation, the ceiling construction functions as
a “pass through system” where moisture readily flows through it from the roof cavity to the indoor
environment where it is removed by the air conditioning equipment. However, when roof cavity
vents were present, the surface relative humidity rose above the critical 80% relative humidity for
about a 1-month period. Before leaving this section, it is worth mentioning that the surface relative
humidities in other parts of the construction were below the critical 80% level. In addition, the
source of moisture in a hot and humid climate is the outdoor environment, as opposed to the indoor
environment for cold climate applications.
The above results indicate that ceiling vapor retarders and roof cavity vents should not be installed
in homes exposed to hot and humid climates.
46
RECOMMENDATIONS FOR FURTHER STUDY
Model Verification
A strong need exists to carry out a field experiment to verify the accuracy of the new MOIST Attic
Model. The attic of a test house would be instrumented to measure the moisture content of the roof
sheathing as a function of time. The outdoor boundary conditions (i.e., outdoor temperature, relative
humidity, wind speed, wind direction, and horizontal solar radiation) would be measured as a
function of time. In addition, special tests would be conducted to develop semi-empirical correlations
that relate the attic air exchange rate to the outdoor wind speed and wind direction, and a separate
semi-empirical correlation would be developed that predicts the airflow from the house into the attic.
The moisture and heat transfer properties of the building materials would be independently
measured. The moisture content of the roof sheathing would be measured as a function of time and
compared to corresponding predicted values.
Roof Moisture Performance in Different U.S. Climates
The results of this report clearly show that similar roofs do not perform alike in different climates
of the U.S. For example, utilizing attic ventilation and a ceiling vapor retarder is a good idea in
northern cold climates, and yet it is not wise in hot and humid climates. Thus, HUD should not
uniformly require attic ventilation and a ceiling vapor retarder in all climates of the U.S. as it now
does. In order to clearly decide which distinct climatic regions should have which requirements and
which should not, it would be worthwhile repeating the type of modeling undertaken in this report
for a larger number of climates across the nation. For example, no modeling has been done for
Alaska or Hawaii, or for mixed climates such as those of the southwest (Texas, Arizona, or southern
California) or for mixed climates such as Arkansas or Tennessee. In addition, concurrent with
examining moisture conditions, it would be worthwhile to look at energy use considerations (heat
loss or gain through ceilings) in making decisions about HUD Standards revisions. The new model
can be used to examine ceiling heat flux values for different roof conditions or constructions.
Uncertainties Regarding Attic Ventilation
The attic simulation model described and applied herein appears to be a valuable new tool for
investigating potential attic moisture problems in manufactured housing. One weakness in the model
is the lack of field data regarding leakage areas and especially the amount of air flow through attic
cavities. The air exchange rate between the attic cavity and the outdoors was modeled using the LBL
natural infiltration model (Sherman and Grimsrud 1980) with stack and wind coefficients obtained
from measurements on twenty “site-built” houses. Typical manufactured housing is generally
characterized by shallower roof pitches and lower attic volumes, as well as fairly airtight ceilings,
and so the attic ventilation characteristics may be quite different than for site-built homes.
Unfortunately, there are no known field data available for attic air exchange rates in manufactured
homes. Such data are clearly needed.
47
In addition, better information is needed on the amount of unintentional roof leakage area in
manufactured homes. There also is uncertainty about the typical ELA values of ceilings in
manufactured homes. Moreover, the impact of the attic stack effect in hot and humid climates also
warrants further investigation. It was neglected in this study based on cold climate Canadian data
(Buchan, Lawton, Parent Ltd 1991). Yet attic modeling by Parker, Fairey, and Gu (1991) showed
that buoyancy effects in attics in hot and humid climates may be important. Their analysis indicated
that buoyancy was important in properly describing energy flows, but they did not focus on moisture
transfer. These issues merit further investigation.
It would be most worthwhile to fit some manufactured homes with different commonly used attic
ventilation systems and measure the air exchange rates with tracer gases over both short and long
time periods. The field data could then be broken down to determine typical stack and wind
coefficients for the LBL infiltration model for each type of ventilation. It also would be important
to try to determine the impact of wind direction in such a study. Further, based on the results of this
study, it would be most important to monitor the attics under conditions with high moisture
generation rates inside the homes that would most likely lead to adverse conditions in the attics or
roof sheathing.
Finally, there are still some prominent building scientists who believe that roofs should not be
ventilated. To unequivocally decide whether it is better to ventilate or not, it would be extremely
worthwhile to test two manufactured houses side by side. One would have attic ventilation and the
other would not. A comparison of their roof sheathing moisture contents would hopefully settle this
issue once and for all.
Shingle Temperature
Building scientists and others associated with the building industry would like to know the effect of
roof ventilation on the temperature of roof sheathing and roof coverings such as asphalt shingles.
This is true for roofs with both open attics above flat ceilings and cathedral ceilings. The impact of
roof ventilation and other factors such as the color of the exterior surface of the roof covering as well
as the type of roof covering (e.g., asphalt shingles, shakes, tile, metal, etc.) is also of interest. The
new MOIST Attic Model is well suited to help assess the impact of ventilation and other factors on
roof sheathing temperatures. Thus, it is recommended that such modeling be undertaken.
SUMMARY AND CONCLUSIONS
A new mathematical model, called the MOIST Attic Model, was presented that predicts the transfer
of moisture and heat in roof cavities. This model performs a heat and moisture balance on a roof
cavity at hourly time steps, and includes the storage of moisture and heat at the construction layers.
The airflow from the house through the ceiling construction into the roof cavity is predicted as a
function of time using a stack-effect model. The ventilation rate of the roof cavity with outdoor air
is predicted as a function of wind speed using a semi-empirical model with the roof ELA serving as
an input. The relative humidity in the house below is permitted to vary during the winter and is
48
predicted from a moisture balance of the whole building with the house ELA and indoor moisture
production rate serving as inputs.
The above model was subsequently used to predict the performance of a double-wide manufactured
house constructed in compliance with the current HUD Standards for manufactured housing. This
current-practice house had an interior vapor retarder installed in its ceiling construction, and the roof
cavity vents were installed consistent with the 1/300 rule. The moisture content of the plywood roof
sheathing was predicted as a function of time of year, and the effect of a wide range of parameters
on the peak moisture content was investigated. Most of the simulations were carried out in
Madison (WI), although a series were carried out in different climates of the United States.
During the winter, the airflow from the house into the roof cavity was found to be the dominant
mechanism for transporting moisture into the roof cavity. Water vapor diffusion was found to play
a considerably less important role. Computer simulations of identical current-practice houses with
and without a vapor ceiling retarder showed only a small difference in roof sheathing moisture
content. A ceiling vapor retarder was found to have a small effect because airflow from the house
into the roof cavity was the dominant moisture transport mechanism. On the other hand, a much
larger difference in roof sheathing moisture content occurred when the airflow from the house into
the roof cavity was varied as a result of the ceiling air tightness.
Passive attic ventilation was found to be a very effective moisture control practice in non-humidified
houses. When roof cavity vents consistent with the 1/300 rule were installed in the current-practice
house in Madison (WI), (as required by the HUD standards), the peak moisture content of the
plywood roof sheathing rose to only 16% during the winter. This peak moisture content was well
below fiber saturation (28%). On the other hand, when the roof cavity vents were not present, the
peak moisture content rose almost to fiber saturation. The analysis further revealed that the peak roof
sheathing moisture content in houses without roof cavity vents can rise considerably above fiber
saturation when the indoor relative humidity is elevated as in the case of a humidified house or a
house having tighter construction and a high indoor moisture production rate. Roof sheathing
moisture content above fiber saturation is believed to pose a risk of material degradation and
shortened service life, especially if the plywood is wet in warm spring and summer periods.
The current HUD Standards permit attic mechanical ventilation at a rate of 0.00010 m3/s per m2
(0.02 ft3/min per ft2 ) of attic floor area to be used instead of roof cavity vents. When the model
simulated the performance of a current practice house with this mechanical ventilation rate, the roof
sheathing moisture content rose to fiber saturation during the winter. This was because the
mechanical ventilation rate was too small. A mechanical ventilation rate of 0.0005 m3/s per m2 (0.1
ft3/min per ft2 ) of attic floor area was found to provide satisfactory performance. It is recommended
that HUD revise the specified mechanical rate for roof cavities.
The computer simulations showed that houses with higher indoor relative humidity have higher roof
sheathing moisture content. Elevated indoor relative humidity occurs in houses that have high
moisture production rates, tight building envelopes, and/or humidification. When the current practice
49
house was humidified at an indoor relative humidity of 45% during the winter in Madison (WI),
moisture content of the north sloping plywood roof sheathing rose to a peak of 25% and approached
fiber saturation (28%). When the roof cavity vents were not present, the model predicted roof
sheathing moisture contents considerably above fiber saturation in the humidified house. Such wet
roof sheathing could potentially degrade.
The practice of providing whole house ventilation by ventilating indoor air (through ceiling vents)
into a roof cavity without roof cavity vents was found to cause elevated roof sheathing moisture
contents that approached fiber saturation in houses located in Madison, WI. The problem of high
roof sheathing moisture content is somewhat diminished by lower indoor relative humidities
produced by the additional whole house ventilation. Another negative attribute is that this practice
imposes a space heating energy penalty on the house. Over the course of the heating season, the
authors calculated that 1,520 kWh would be required to heat incoming ventilation air in an
electrically heated house. At 6.4 cents per kWh, the energy penalty for providing this additional
whole house ventilation would be ninety-seven dollars ($97) per year.
The coldness of the outdoor climate was found to have much less effect on the sheathing moisture
content than reported in a previous study. In the present study, the indoor relative humidity was
permitted to vary during the winter and was calculated from a moisture balance of the whole
building. The roof sheathing moisture contents tended to lie within a narrow range. In the previous
study, the indoor relative humidity was maintained at a constant level in all the simulations, and the
roof sheathing moisture content increased markedly with the coldness of the outdoor climate. The
effect of climate is diminished in the present study because lower indoor relative humidities occur
in colder climates, which decreases the indoor potential (i.e. water-vapor pressure) for moisture
transport into the roof cavity.
In non-humidified houses, the current moisture control practices given in the HUD Standards (i.e,
installing an interior vapor retarder in the ceiling construction and installing roof cavity vents
consistent with the 1/300 rule) were found to be effective in cold climates. That is, the peak moisture
content of the roof sheathing was always well below fiber saturation in non-humidified houses of
tighter construction with high indoor moisture generation rates. However, in humidified houses,
some houses with roof cavity vents may experience roof sheathing moisture contents above fiber
saturation during the winter months. Even in those cases, the roof sheathing dried out satisfactorily
during the spring and early summer when wood temperatures are high enough for decay to occur.
Thus, structural damage is unlikely.
These same moisture control practices did not result in acceptable performance in hot and humid
climates. When a vapor ceiling retarder was present, moisture from the outdoor environment
accumulated at its upper surface where the relative humidity rose above the critical 80% level
conducive to mold and mildew growth. Higher surface relative humidities at the vapor retarder
occurred in houses with roof cavity vents. In houses exposed to hot and humid climates, it may be
wise not to install a ceiling vapor retarder and roof cavity vents. It is particularly important to avoid
installing a ceiling vapor retarder.
50
It is recommended that field studies be conducted to experimentally corroborate the above theoretical
results prior to making revisions to the HUD Standards for manufactured housing.
ACKNOWLEDGMENTS
The authors thank William Freeborne of the Division of Affordable Housing, Research, and
Technology of the U.S. Department of Housing and Urban Development for funding this project and
making many helpful suggestions during the review of the report. The authors would like to thank
Walter Rossiter and Dale Bentz for providing many helpful suggestions during the review of the
report. The authors would also like to thank Paula Svincek for preparing this manuscript for
publication, and Ray Mele for preparing the figures for publication.
51
NOMENCLATURE
Symbol
Af
An
B1, B2, B3
c
C1, C2, C3
Cv,c
Cv,h
C T,c
C T,h
D
E
hlv
hc,i
hc,n
hc,o
hr,i
hr,o
Hc
Hh
Hsol
k
K
Lc
Le
Lh
Lw
Lr
mn
Me,i
Mf,i
Mp,i
n
N
pl
pv
pv,i
pv,c
pv,n
pr
pt
t
T
SI
Units
m2
m2
J/kg@K
(L/s)2@cm-4@(m/s)-2
(L/s)2@cm-4@(m/s)-2
(L/s)2@cm-4@K-1
(L/s)2@cm-4@K-1
m2/s
J/kg
W/m2@K
W/m2@K
W/m2@K
W/m2@K
W/m2@K
m
m
W/m2
W/m@K
kg/m@s@Pa
m2
m2
m2
m2
m2
kg/m2@s@Pa
kg/m2@s@Pa
kg/m2@s@Pa
kg/m2@s@Pa
Pa
Pa
Pa
Pa
Pa
Pa
Pa
s
EC
English
Units
ft2
ft2
Btu/lb@ER
cfm2/in.4@mph2
cfm2/in.4@mph2
cfm2/in.4@EF
cfm2/in.4@EF
ft2/h
Btu/lb
Btu/h@ft2@ER
Btu/h@ft2@ER
Btu/h@ft2@ER
Btu/h@ft2@ER
Btu/h@ft2@ER
ft
ft
Btu/h@ft2
Btu/h@ft@ER
lb/ft@h@inHg
ft2
ft2
ft2
ft2
ft2
lb/ft2@h@inHg
lb/ft2@h@inHg
lb/ft2@h@inHg
lb/ft2@h@inHg
inHg
inHg
inHg
inHg
inHg
inHg
inHg
h
EF
52
Definition
House floor area
Area of surface n
Constants in sorption isotherm equation
Specific heat
Constants in permeability equation
Wind coefficient for roof cavity
Wind coefficient for house
Stack coefficient for roof cavity
Stack coefficient for house
Liquid diffusivity
Emittance factor
Latent heat of vaporization
Convective heat transfer coef. at inside surf.
Convective heat transfer coef. at surface n
Convective heat transfer coef. at outside surf.
Radiative heat transfer coef. at inside surf.
Radiative heat transfer coef. outside surf.
Stack height for roof cavity
Stack height for house
Incident solar radition onto a surface
Thermal conductivity
Hydraulic conductivity
Effective leakage area for ceiling construction
Effective leakage area for stack effect airflow
Effective leakage area for whole house
Effective leakage area for house exterior walls
Effective leakage area for roof construction
Mass transfer coefficient at surface n
Effective inside surface permeance
Air film permeance at inside surface
Paint permeance at inside surface
Hourly summation index
Current hour
Capillary pressure
Water vapor pressure
Water vapor pressure of indoor air
Water vapor pressure of cavity air
Water vapor pressure at surface n
Stack-effect reference pressure (4 Pa)
Total stack-effect pressure
Time
Temperature
Symbol
Tc
Ti
Tm
Ts,n
Tsky
To
v
v0 c
v0 häc
v0 h,m
v0 h,n
v0 h,t
y
w
0
Z(n)
M
T
a
d
µ
i
i,
c
i
o
SI
Units
EC
EC
EC
EC
EC
EC
m/s
m3/s
m3/s
m3/s
m3/s
m3/s
m
kg/s
kg/kg
kg/s@m2
kg/m3
kg/m3
W/m2@K4
kg/m@s@Pa
s
kg/kg
kg/kg
kg/kg
English
Units
EF
EF
EF
EF
EF
EF
mi/h
ft3/min
ft3/min
ft3/min
ft3/min
ft3/min
ft
lb/h
lb/lb
lb/h@ft2
lb/ft3
lb/ft3
Btu/h@ft2E@R4
lb/h@ft@inHg
h
lb/lb
lb/lb
lb/lb
53
Definition
Cavity air temperature
Indoor temperature
Mean temperature between the surface and sky
Temperature of surface n
Sky temperature
Outdoor air temperature
Average wind speed
Outdoor cavity ventilation rate
Airflow rate from house to cavity
House mechanical ventilation rate
House natural ventilation rate
Total house ventilation rate
Distance
Moisture generation rate
Exponential weighting factors
Moisture content on dry mass basis
Convergence criteria for moisture solution
Convergence criteria for thermal solution
Sorption constant per unit floor area
Air density
Dry material density
Stefan-Boltzmann constant
Water vapor permeability
Moisture storage time constant
Relative humidity
Indoor relative humidity
Indoor hygric memory
Cavity air humidity ratio
Indoor air humidity ratio
Outdoor air humidity ratio
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